Colloquium Abstract: Dr. Ted Cox, Mathematics, UBC

The Voter Model: a survey and some recent results

The voter model, closely related to the stepping stone model of
mathematical genetics, was introduced independently by Clifford
and Sudbury in 1973 and Holley and Liggett in 1975. It is a
stochastic process designed to model the evolution of a
spatially distributed population whose individuals hold
various "opinions" and try, at random times, to influence
the opinions of nearby individuals. (Alternatively, one can
think of individuals of various species who try to "colonize"
nearby sites.) The voter model is one of the most mathematically
tractable of a class of stochastic processes called interacting
particle systems. In this talk, I will describe some of the basic
features of the model, and present some recent work motivated by
questions on "species abundance" distributions. Technology willing,
the talk will include some computer simulations.